You can feel free to keep running that internal Exchange server folks:
If you implement a single sign-on solution, we strongly recommend that you maintain at least one Exchange server so that you can access Exchange System Manager (Exchange 2003) or the Exchange Management Console/Exchange Management Shell (Exchange 2007, Exchange 2010, and Exchange 2013) to manage mail-related attributes on the on-premises mail-enabled users. For Exchange 2007 and Exchange 2010, the Exchange server that you maintain should have the Hub Transport, Client Access, and Mailbox server roles installed.
Role over - http://technet.microsoft.com/en-us/library/jj874016(v=exchg.150).aspx
Of course, that directly contradicts the migration article:
Step 5 Implement a single sign-on solution (optional) After all mailboxes are migrated to the cloud, you can implement a single sign-on solution to enable users to use their on-premises Active Directory credentials (username and password) to access their Office 365 mailboxes and existing on-premises resources. You implement a single sign-on solution by deploying Active Directory Federation Services (AD FS) 2.0 (AD FS 2.0). For more information, see Cutover Exchange Migration and Single Sign-on. Step 6 Remove your on-premises Exchange organization (optional) After you’ve verified that all email is being routed directly to the cloud-based mailboxes, completed the migration, and no longer need to maintain your on-premises email organization or don’t plan on implementing a single sign-on solution, you can uninstall Exchange from your servers and remove your on-premises Exchange organization. For more information, see the following:
See the following, you betcha: http://technet.microsoft.com/en-us/library/jj159539.aspx
Here are the bits that MS says get synched:
Table 1: Attributes that are synced from the on-premises Active Directory Domain Services (AD DS) to Windows Azure Active Directory (Windows Azure AD) The following table lists the attributes that are synced from the on-premises AD DS to Windows Azure AD. Be aware that objects must contain values in the following attributes to be considered for sync: cn member (applies only to groups) samAccountName (applies only to users) alias (applies only to groups and contacts) displayName (for groups with an mail or proxyAddresses attribute populated) Synced object attribute User Group Contact (Src) Description assistant Read - Read The name of the assistant for an account. authOrig Read Read Read Relationship that indicates that the mailbox for the target object is authorized to send mail to the source object. C - - Read Two-letter ISO 3166 [ISO3166] country code. cn Read Read Read co Read - Read The country/region in which the person (user or contact) or company is located. company Read - Read The person's (user or contact) company name. countryCode Read - Read The country code for person's (user or contact) language of choice. department Read - Read The name of the person's (user or contact) department. description Read Read Read Human-readable descriptive phrases about the object. displayName Read Read Read The display name for an object, usually the combination of the person's first name, middle initial, and last name. dLMemRejectPerms Read Read Read Relationship that indicates that members of the target object are -t authorized to send mail to the source object. dLMemSubmitPerms Read Read Read Relationship that indicates that members of the target object are authorized to send mail to the source object. ExtensionAttribute1 Read Read Read Custom attribute that is defined in the customer on-premises directory. ExtensionAttribute10 Read Read Read Custom attribute that is defined in the customer on-premises directory. ExtensionAttribute11 Read Read Read Custom attribute that is defined in the customer on-premises directory. ExtensionAttribute12 Read Read Read Custom attribute that is defined in the customer on-premises directory. ExtensionAttribute13 Read Read Read Custom attribute that is defined in the customer on-premises directory. ExtensionAttribute14 Read Read Read Custom attribute that is defined in the customer on-premises directory. ExtensionAttribute15 Read Read Read Custom attribute that is defined in the customer on-premises directory. ExtensionAttribute2 Read Read Read Custom attribute that is defined in the customer on-premises directory. ExtensionAttribute3 Read Read Read Custom attribute that is defined in the customer on-premises directory. ExtensionAttribute4 Read Read Read Custom attribute that is defined in the customer on-premises directory. ExtensionAttribute5 Read Read Read Custom attribute that is defined in the customer on-premises directory. ExtensionAttribute6 Read Read Read Custom attribute that is defined in the customer on-premises directory. ExtensionAttribute7 Read Read Read Custom attribute that is defined in the customer on-premises directory. ExtensionAttribute8 Read Read Read Custom attribute that is defined in the customer on-premises directory. ExtensionAttribute9 Read Read Read Custom attribute that is defined in the customer on-premises directory. facsimiletelephonenumber Read - Read Telephone numbers (and, optionally, the parameters) for facsimile terminals. givenName Read - Read Name strings that are the part of a person's (user or contact) name that is -t their surname. GroupType - Read - hideDLMembership - Read - Hide the membership list on a distribution list from senders. homephone Read - Read The person's (user or contact) main home telephone number. info Read Read Read Initials Read - Read Strings of initials of some or all of an individual's names, except the surname(s). ipPhone Read - Read The TCP/IP address for the telephone. l Read - Read Names of a locality or place, such as a city, county, or other geographic region. legacyExchangeDN Read Read Read mail Read Read Read The list of email addresses for a person (user or contact). mailnickname Read Read Read managedBy - Read - Resource/owner relationship, where the source object (a group) is the resource, and the target object is the owner. manager Read - Read Manager/direct report relationship between two individuals, where the source object is the direct report, and the target object is the manager. member - Read - Membership of the target object (of class User, Contact, or Group) in the group that is identified as the source object. middleName Read - Read Additional names for a person (user or contact), for example, middle name, patronymic, matronymic, or other names. mobile Read - Read The primary mobile phone number for a person (user or contact). msDS-HABSeniorityIndex Read Read Read msDS-PhoneticDisplayName Read Read Read MsExchArchiveGUID Read - - MsExchArchiveName Read - - msExchArchiveStatus Read/Write - - Created in the Exchange cloud for "write back" to on-premises when the customer has a cloud archive. msExchAssistantName Read - Read The name of the assistant for an account. msExchAuditAdmin Read - - msExchAuditDelegate Read - - msExchAuditDelegateAdmin Read - - msExchAuditOwner Read - - MsExchBlockedSendersHash Read/Write - Read Populated through an upgrade from Business Productivity Online Standard Suite. –t synced from on-premises. msExchBypassAudit Read - - MsExchBypassModerationFromDLMembersLink Read Read Read MsExchBypassModerationLink Read Read Read msExchCoManagedByLink - Read - msExchDelegateListLink Read - - msExchELCExpirySuspensionEnd Read - - msExchELCExpirySuspensionStart Read - - msExchELCMailboxFlags Read - - MsExchEnableModeration Read Read - msExchExtensionCustomAttribute1 Read Read Read msExchExtensionCustomAttribute2 Read Read Read msExchExtensionCustomAttribute3 Read Read Read msExchExtensionCustomAttribute4 Read Read Read msExchExtensionCustomAttribute5 Read Read Read MsExchGroupDepartRestriction - Read - MsExchGroupJoinRestriction - Read - msExchHideFromAddressLists Read Read Read Indicator to control the visibility of a mail recipient for name resolution. MsExchImmutableID Read - - msExchLitigationHoldDate Read Read Read msExchLitigationHoldOwner Read Read Read MsExchMailboxGuid Read - - The GUID of the user’s mailbox. msExchMailboxAuditEnable Read - - msExchMailboxAuditLogAgeLimit Read - - MsExchModeratedByLink Read Read Read MsExchModerationFlags Read Read Read MsExchRecipientDisplayType Read Read Read msExchRecipientTypeDetails Read Read Read MsExchRemoteRecipientType Read - - msExchRequireAuthToSendTo Read Read Read When enabled for a distribution list (DL), unauthenticated users are rejected. MsExchResourceCapacity Read - - MsExchResourceDisplay Read - - MsExchResourceMetaData Read - - MsExchResourceSearchProperties Read - - msExchRetentionComment Read Read Read msExchRetentionURL Read Read Read MsExchSafeRecipientsHash Read/Write - Read Populated through an upgrade from Business Productivity Online Standard Suite. -t synced from on-premises. MsExchSafeSendersHash Read/Write - Read Populated through an upgrade from Business Productivity Online Standard Suite. -t synced from on premises. MsExchSenderHintTranslations Read Read Read msExchTeamMailboxExpiration Read - - msExchTeamMailboxOwners Read - - msExchTeamMailboxSharePointLinkedBy Read - - msExchTeamMailboxSharePointUrl Read - - msExchUCVoiceMailSettings Read/Write - - msExchUsageLocation Read - - msExchUserHoldPolicies Read/Write - - Litigation Hold allows cloud services to determine which users are under Litigation Hold msOrg-IsOrganizational - Read - msRTCSIP-ApplicationOptions Read - - msRTCSIP-DeploymentLocator Read - Read Fully qualified DNS name of the Microsoft Lync Server 2010 deployment, as specified in the authoritative (customer, on-premises) directory. msRTCSIP-Line Read - Read The device ID (either the Session Initiation Protocol (SIP) uniform resource identifier (URI) or the TEL URI) of the telephone that the user controls. msRTCSIP-OwnerUrn Read - - msRTCSIP-PrimaryUserAddress Read - Read SIP URI for instant messaging, as specified in the authoritative (customer, on-premise) directory. msRTCSIP-UserEnabled Read - Read Indicates whether the user is currently enabled for SIP instant messaging, as specified in the authoritative (customer, on-premises) directory. msRTCSIP-OptionFlags Read - Read objectGUID Read Read Read Key for the object: this key is immutable, even if the object moves from one context to another, for example, as a result of a company merge or split. oOFReplyToOriginator - Read - Governs whether out-of-office -tifications should be sent to a sender of a message to this distribution list (DL). otherFacsimileTelephone Read - Read A list of alternative facsimile numbers. otherHomePhone Read - Read A list of alternative home telephone numbers. otherIpPhone Read - Read A list of alternative TCP/IP addresses for the telephone. otherMobile Read - Read A list of alternative mobile phone numbers. otherPager Read - Read A list of alternative pager numbers. otherTelephone Read - Read A list of alternative office telephone numbers. pager Read - Read The primary pager number. photo Read - - physicalDeliveryOfficeName Read - Read Names that a postal service uses to identify a post office. postalCode Read - Read Codes that a postal service uses to identify postal service zones. postOfficeBox Read - Read Postal box identifiers that a postal service uses when a customer arranges to receive mail at a box on the premises of the postal service. PreferredLanguage Read - - The preferred written or spoken language for a user. proxyAddresses Read/Write Read/Write Read/Write The address by which a Microsoft Exchange Server recipient object is recognized in a foreign mail system. PublicDelegates Read/Write Read Read Cross-premises public delegation: allows users to specify delegates for their mailbox. reportToOriginator - Read - Governs whether to send delivery reports to the message originator when a message that is sent to a group is -t delivered. The delivery report lets the group owner k-w that the message was -t delivered. ReportToOwner - Read - samAccountName Read - - sn Read - Read Name strings for the family names of a person (user or contact). st Read - Read The full names of states or provinces. streetAddress Read - Read The person's (user or contact) address. targetAddress Read - Read The destination address for the person (user or contact). TelephoneAssistant Read - Read telephoneNumber Read - Read Telephone numbers that comply with the ITU Recommendation E.123. thumbnailphoto Read - Read Persons Photo - 10kb maximum size limit title Read - Read The title of a person (user or contact) in the person's organizational context. unauthOrig Read Read Read Relationship that indicates that the mailbox for the target object is -t authorized to send mail to the source object. url Read - Read The list of alternative web pages. userAccountControl Read - - UserPrincipalName Read Read - The user principal name (UPN) that is an Internet-style logon name for a user, as specified in RFC 822. wWWHomePage Read - Read The primary web page.
Credit to that pile of LDAP goes to this link : http://support.microsoft.com/kb/2256198